Solutions of Inviscid Burgers’ and Equal Width Wave Equations by RDTM

Abstract

 Abstract—In this paper, the Reduced Differential Transform method (RDTM) is used to find the numerical solution of the equal width wave (EW) equation and the exact analytical solution of the inviscid Burgers' equation with initial conditions. The method has been used successfully to investigate the motion of a single solitary wave that is governed by the EW equation. The solution is obtained in the form of convergent power series. The results obtained show that the error norms to the exact solutions are reasonably small and that the present method is easier and powerful than some other known techniques. It is commonly known that the equations of gas dynamics are the mathematical expressions of conservation laws which exist in engineering physics such as conservation of mass, conservation of momentum, conservation of energy etc. The inviscid equation of gas dynamics can be written in the conservation form which is a nonlinear partial differential equation. Partial differential equations have numerous applications in various fields such as fluid mechanics, physics, thermodynamics etc. Most of these equations are nonlinear partial differential equations. A broad class of analytical solution methods and numerical solution methods were applied to solve these partial differential equations by Morrison et al. (1), Gardner and Gardner (2), Smith (3), Courant and Friedrichs (4), Evans and Bulut (5), Wazwaz ((6) and (7)), He ((8) and (9)), Keskin (10), Peregrine (11), Bluman and Kumei (12), Whitham (13), Hunter and Keller (14), He and Moodie (15), Sharma and Radha (16), Sharma and Srinivasan (17) and Arora and Sharma (18) etc.wave equation. The equal width wave equation, introduced by Morrison et al. (1), is of great importance since it is used as a model partial differential equation for the simulation of one dimensional wave propagation in nonlinear media with dispersion process. In this Paper, we shall consider the Inviscid Burgers' equation